
The \(f_{\mathrm {min}}\)  is chosen from the frequency band of detector, then \(f_{\mathrm {max}}\)  can be obtained from Eq. (REF ). The typical observation time has been shown as dashed line in Fig. REF . The shadow regions above dashed lines show detectable mass ranges of detectors within the observation time. We can find dashed lines are not monotonic, which is caused by the redshift bias effect. According to Eq. (REF ) and (REF ), optimal SNR function is monotonically decreasing for \(z < 2.63\)  and increasing for \(z > 2.63\)  in our \(\Lambda \mathrm {CDM}\)  universe [1]}, for detecting the signal with \(\mathrm {S/N} = 8\) , the chirp mass of PBH binary need increase for \(z < 2.63\)  and decrease for \(z > 2.63\) .
